• Title/Summary/Keyword: vibration energy governing equation

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Optimal Design of MR Suspension Unit for Tracked Vehicle (궤도 차량용 MR 현수장치의 최적 설계)

  • Ha, Sung-Hoon;Kim, Hyung-Seob;Choi, Seung-Bok;Woo, Je-Kwan
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.21 no.6
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    • pp.499-505
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    • 2011
  • This paper presents optimal design of controllable magnetorheological suspension unit for a tracked vehicle. As a first step, a double-rod type MR suspension unit is designed on the basis of the Bingham model of commercially available MR fluid, and its damping characteristics are evaluated with respect to the intensity of the magnetic field. Subsequently, the governing equation of motion of the MR suspension system featuring the MR valve is established. Then, the optimization problem to find optimal geometric dimensions of the MR supension unit is formulated by considering an objective function which is related to damping torque and control energy. The first order optimization method intergrated with a commercial finite element method(FEM) software is adopted to obtain optimal solution of the system. The performance characteristics of the optimized MR susepnsion unit is then evaluated and compared with initial one.

Mechanical analysis of cutout piezoelectric nonlocal nanobeam including surface energy effects

  • Eltaher, Mohamed A.;Omar, Fatema-Alzahraa;Abdalla, Waleed S.;Kabeel, Abdallah M.;Alshorbagy, Amal E.
    • Structural Engineering and Mechanics
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    • v.76 no.1
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    • pp.141-151
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    • 2020
  • This manuscript tends to investigate influences of nanoscale and surface energy on a static bending and free vibration of piezoelectric perforated nanobeam structural element, for the first time. Nonlocal differential elasticity theory of Eringen is manipulated to depict the long-range atoms interactions, by imposing length scale parameter. Surface energy dominated in nanoscale structure, is included in the proposed model by using Gurtin-Murdoch model. The coupling effect between nonlocal elasticity and surface energy is included in the proposed model. Constitutive and governing equations of nonlocal-surface perforated Euler-Bernoulli nanobeam are derived by Hamilton's principle. The distribution of electric potential for the piezoelectric nanobeam model is assumed to vary as a combination of a cosine and linear variation, which satisfies the Maxwell's equation. The proposed model is solved numerically by using the finite-element method (FEM). The present model is validated by comparing the obtained results with previously published works. The detailed parametric study is presented to examine effects of the number of holes, perforation size, nonlocal parameter, surface energy, boundary conditions, and external electric voltage on the electro-mechanical behaviors of piezoelectric perforated nanobeams. It is found that the effect of surface stresses becomes more significant as the thickness decreases in the range of nanometers. The effect of number of holes becomes significant in the region 0.2 ≤ α ≤ 0.8. The current model can be used in design of perforated nano-electro-mechanical systems (PNEMS).

Two-stage crack identification in an Euler-Bernoulli rotating beam using modal parameters and Genetic Algorithm

  • Belen Munoz-Abella;Lourdes Rubio;Patricia Rubio
    • Smart Structures and Systems
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    • v.33 no.2
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    • pp.165-175
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    • 2024
  • Rotating beams play a crucial role in representing complex mechanical components that are prevalent in vital sectors like energy and transportation industries. These components are susceptible to the initiation and propagation of cracks, posing a substantial risk to their structural integrity. This study presents a two-stage methodology for detecting the location and estimating the size of an open-edge transverse crack in a rotating Euler-Bernoulli beam with a uniform cross-section. Understanding the dynamic behavior of beams is vital for the effective design and evaluation of their operational performance. In this regard, modal parameters such as natural frequencies and eigenmodes are frequently employed to detect and identify damages in mechanical components. In this instance, the Frobenius method has been employed to determine the first two natural frequencies and corresponding eigenmodes associated with flapwise bending vibration. These calculations have been performed by solving the governing differential equation that describes the motion of the beam. Various parameters have been considered, such as rotational speed, beam slenderness, hub radius, and crack size and location. The effect of the crack has been replaced by a rotational spring whose stiffness represents the increase in local flexibility as a result of the damage presence. In the initial phase of the proposed methodology, a damage index utilizing the slope of the beam's eigenmode has been employed to estimate the location of the crack. After detecting the presence of damage, the size of the crack is determined using a Genetic Algorithm optimization technique. The ultimate goal of the proposed methodology is to enable the development of more suitable and reliable maintenance plans.